BEIJING, Jan 1(Reuters) - China's home prices fell at a faster pace in December, according to a private survey on Sunday, reflecting persistently weak demand amid rising COVID-19 cases despite a slew of support measures.

China's property market crisis worsened this summer, with official data showing home prices, sales and investment all falling in recent months, adding pressure on the faltering economy.

Home prices in 100 cities fell for the sixth month in a row in December, declining 0.08% from a month earlier after falling 0.06% in November, according to the survey by China Index Academy (CIA), one of the country's largest independent real estate research firms.

Among the 100 cities, 68 cities posted a fall in monthly prices, compared with 57 in November, the survey showed.

China has in recent weeks ramped up support for the industry in a bid to relieve a long-running liquidity squeeze that has hit developers and delayed completion of many housing projects, further undermining buyers' confidence. The moves have included lifting a ban on fundraising via equity offerings for listed property firms.

The property sector has also got a slight boost after Beijing abruptly dropped its strict zero-COVID policy in early December, which could lure consumers back to showrooms. But the virus is now spreading largely unchecked and likely infecting millions of people a day, according to some international health experts.

"Real estate policies may continue to maintain an accommodative tone with room for policy easing on the supply and demand side in 2023," said the real estate research firm, adding "the housing market is expected to stabilize gradually next year." (Reporting by Liangping Gao and Ryan Woo; Editing by Kim Coghill)